Magnetic skyrmions are topologically protected spin textures typical of chiral magnets characterized
by a special kind of exchange interaction known as Dzyaloshinkii-Moriya interaction (DMI).
In the last years growing interest has been addressed to the study of these topological defects both
from a fundamental point of view and for its several technological applications like for instance
their usage as information carriers [1]. Great attention has been also given to skyrmion nucleation,
stability and motion in confined magnetic systems under the influence of a spin-current [2,3].
Recently, the effect of confinement has been studied in the presence of spin-polarized current [2],
but there are not yet studies focusing on the skyrmion motion driven by SHE in constrained
geometries.
Here, we solve analytically Thiele’s equation in the presence of spin-Hall effect (SHE) with no
external field and by taking into account confinement. The spin-Hall current injected in the heavy
metal along the x direction (see Fig.1 (a)) combined with the interfacial DMI favors the Néel skyrmion
(hedgehog-like) nucleation in a thin magnetized stripe. We model confinement effects by
introducing a potential V(r) which arises at the boundaries of the magnetic stripe. This potential can
be thought of as a positive barrier having a repulsive nature associated to the static magnetization
rotation at the stripe borders. The Nèel skyrmions is interpreted as a quasi-particle which interacts
repulsively with this barrier. As a result, its trajectory is deviated.

Magnetic skyrmions are topologically protected spin textures typical of chiral magnets characterized
by a special kind of exchange interaction known as Dzyaloshinkii-Moriya interaction (DMI).
In the last years growing interest has been addressed to the study of these topological defects both
from a fundamental point of view and for its several technological applications like for instance
their usage as information carriers [1]. Great attention has been also given to skyrmion nucleation,
stability and motion in confined magnetic systems under the influence of a spin-current [2,3].
Recently, the effect of confinement has been studied in the presence of spin-polarized current [2],
but there are not yet studies focusing on the skyrmion motion driven by SHE in constrained
geometries.
Here, we solve analytically Thiele’s equation in the presence of spin-Hall effect (SHE) with no
external field and by taking into account confinement. The spin-Hall current injected in the heavy
metal along the x direction (see Fig.1 (a)) combined with the interfacial DMI favors the Néel skyrmion
(hedgehog-like) nucleation in a thin magnetized stripe. We model confinement effects by
introducing a potential V(r) which arises at the boundaries of the magnetic stripe. This potential can
be thought of as a positive barrier having a repulsive nature associated to the static magnetization
rotation at the stripe borders. The Nèel skyrmions is interpreted as a quasi-particle which interacts
repulsively with this barrier. As a result, its trajectory is deviated.